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Overview Continued
Fourth
grade quarter
2 mathematics focuses on basic facts and computation with larger numbers, problem
solving strategies, geometry, and perimeter and area.
As fourth graders you will experience math problems involving real world
situations, basic facts review through 12, perimeter and area of squares
and rectangles, and develop problem-solving strategies. You will
understand the importance of place value in computation with larger
numbers, expand strategies for
problem solving, and experience geometry that includes the difference between perimeter
and area. You will continue to deepen your understanding of the
use and importance of mathematics in the world around us.
Quarter 3 of fourth grade focuses on fractions, patterns, prediction
with probability, problem solving strategies, place value in decimals, and
computation. You will experience math problems involving
real world situations; fractional parts of regions, collections of
objects, and wholes using manipulatives and/or visual representations;
recognize and extend more complex patterns; predict outcomes using
coins, spinners, and cubes; identify place values to hundredths in
decimals; and choose appropriate
problem-solving strategies.
In quarter 4 of fourth grade mathematics, you will explore
place value in decimals to the hundredths place; identify and compare
fractional parts of a collection of objects; recognize, complete, and
continue number and shape patterns; use a ruler to measure distance; and
predict, determine, and support which outcomes are most likely, least
likely, or equally likely from flipping a coin, spinning a spinner with 4
congruent sectors, and rolling a number cube.
Enduring Understandings
are important ideas that students should carry with them years beyond the
instruction received this year.
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Numbers
help us make sense of the world around us.
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Numbers can be
represented, ordered, and communicated in many different forms.
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Number
sense
is necessary to solve problems and communicate the reasoning used.
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Communicating mathematical reasoning helps justify solutions.
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Patterns help us make sense of our world and solve problems.
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Fractions and decimals
are parts of a whole and are related.
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Problem solving strategies help us achieve a quality solution.
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Digits have different values according to their place
value.
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Geometric patterns help us solve problems.
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Measurement
tools help us solve a variety of problems.
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Probability and predictions help us determine and support reasonable
solutions.
Essential Questions
are the most important “big picture” questions students should be able to answer
after completing learning activities.
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How
are the skills of estimation and computation related?
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Why
is being able to find different types of patterns in our world
important?
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Why
might we want to show numerical information in a graph, table, or
chart?
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How
are addition and multiplication related?
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In what ways can numbers be
communicated, represented, ordered, and written?
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How does number
sense; estimation, prediction, and mental math, help solve real-world
problems?
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In what ways can I
communicate the reasoning used in problem solving situations?
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What makes for a quality
solution, and what
components are needed to solve real-world problems?
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How
are fractions and decimals related? (How are they the same, and how are
they different?)
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How
does the placement of a digit change number values?
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Why
can we say that all of math is patterns?
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How can patterns (shape, number, and geometric) help
us solve problems?
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Explain how decimals and fractions are parts of a
whole?
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Explain how we use the various tools of measurement.
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Why is it important to understand probability?
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How does prediction help us determine reasonable
answers?
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Why is the vocabulary of probability important? (most
likely, least likely, equally likely, certain, impossible, outcomes)
CSAP
Tested Standards
Highest Frequency
 High
Frequency
 Other
Standards and E-Skills
Highest Frequency = the timing, intensity and
level of accountability is extremely high because mastery of these skills
will must be demonstrated at
this grade level.
High
Frequency = the timing, intensity and level of
accountability is high because mastery of these skills is expected at this grade level.
Other
Standards and E-Skills = the timing, intensity, and level of mastery are
not urgent. It should be introduced during this time so students can
experience the concept and return in future quarters to strive
towards mastery. |
Standard 1: Number Sense - August
 Read,
write and order numbers to hundred thousand
 Recognize
and explain different strategies for estimating and computing.
 Recognize
and explain different strategies for estimating and computing with money.
Standard 4: Geometry - August
Identify,
describe and give examples of congruent shapes.
Identify,
classify and compare 2-dimensional shapes and use vocabulary to describe the
attributes (i.e., number of sides, vertices, angles and parallel sides).
Recognize
and draw lines of symmetry in a given shape.
Identify
a line of symmetry for a given shape.
Standard 5: Measurement - August
Tell
time in hours and minutes, including a.m. and p.m., using analog and digital
displays.
Standard 6: Computation - August
Review
computation without context (addition, subtraction, multiplication, division
facts)
Standard 1: Number Sense - September
Use
and apply estimation strategies to determine reasonable answers when
computing.
Read,
write and order numbers to hundred thousand
Read,
write and identify numbers to the place value of hundred-thousand, include
giving the value of the digits in numeral to the place value of
hundred-thousand.
Recognize
and explain different strategies for estimating and computing.
Generate
equivalent representations for the same number up to 99,999.
Recognize
and explain different strategies for estimating and computing with money.
Standard 2: Patterns and Algebra - September
Reproduce,
extend, create or describe patterns, using pictures, geometric shapes or
numbers.
Standard 3: Data and Graphs - September
Using
statistical landmarks read and interpret tables, line plots, bar graphs and
pictographs.
Use
estimation strategies to determine reasonable answers based on tables, line
plots, bar graphs and pictographs.
Standard 4: Geometry - September
Identify,
describe and give examples of congruent shapes.
Identify,
classify and compare 2-dimensional shapes and use vocabulary to describe the
attributes (i.e., number of sides, vertices, angles and parallel sides).
Recognize and
draw lines of symmetry in a given shape.
Identify a
line of symmetry for a given shape.
Identify
shapes from their attributes.
Name, draw
and label lines and line segments, to include intersecting and parallel
lines.
Standard 5: Measurement - September
Choose
the appropriate tool (e.g., ruler, measuring cups, clock, scale/balance,
thermometer) to measure familiar objects in situations that contain length,
weight, capacity, time and temperature.
Standard 6: Computation - September
Solve
basic multiplication facts through 12.
Solve
basic addition and subtraction problems.
Using
paper and pencil, demonstrate basic operations of whole numbers including
addition and subtraction.
Standard 1: Number Sense - October
Use
and apply estimation strategies to determine reasonable answers when
computing.
Read, write
and identify numbers to the place value of hundred-thousand, include giving
the value of the digits in numeral to the place value of hundred-thousand.
Generate
equivalent representations for the same number up to 99,999.
Recognize a
number from its written version (word form into standard form).
Use a number
line, hundreds chart, or other number chart to locate, label, or count from
any number by 2s, 3s, 5s, 10s or 100s.
Standard 2: Patterns and Algebra - October
Determine
a missing element in a pattern that uses pictures, geometric shapes or
numbers (i.e., solving for the unknown quantity in simple equations in
addition and subtraction).
Use, explain,
and demonstrate the understanding of patterns and missing elements in
problem solving situations.
Standard 3: Data and Graphs - October
Read and
interpret data tables, using the concepts of largest, smallest, most often
and middle.
Using
statistical landmarks read and interpret tables, line plots, bar graphs and
pictographs.
Use
estimation strategies to determine reasonable answers based on tables, line
plots, bar graphs and pictographs.
Standard 4: Geometry - October
Identify,
name, draw and label lines and line segments, to include intersecting and
parallel lines.
Identify,
classify and compare 2-dimensional figures (trapezoids, parallelograms,
rhombus and other polygons)
Name,
draw and label angles, triangles, trapezoids, parallelograms, rhombuses,
quadrangles and other polygons.
Recognize
common attributes of squares and rectangles.
Standard 5: Measurement - October
Compare
objects according to measurable attributes of length and area in US and
metric units.
Standard 6: Computation - October
Solve
basic multiplication facts through 12.
Using paper
and pencil, demonstrate basic operations of whole numbers including addition
and subtraction.
Demonstrate
ability to borrow and carry (trade) in multi-digit addition and subtraction
problems.
Standard 1: Number Sense - November
Compare
large numbers and order 0 – 99,999.
Use
and apply estimation strategies to determine reasonable answers when
computing.
Recognize
different combinations of currency and coins to $10.00.
Use number properties with any of the four basic operations
(commutative, associative, property of zero and one).
Plot decimals on a number line.
Standard 2: Patterns and Algebra - November
Determine
a missing element in a pattern that uses pictures, geometric shapes or
numbers.
Reproduce, create, extend and describe numerical/pictorial patterns
using a number line, a hundreds chart, or other chart to locate, label,
or count from any number by 2s, 3s, 5s, 10s, or 100s.
Display numbers in tables or graphs to show patterns (i.e., completing
an input/output box, T-chart or function box).
Standard 3: Data and Graphs - November
Using
statistical landmarks construct tables, line plots, bar graphs and
pictographs.
Use estimation strategies to determine reasonable answers based on
tables, line plots, bar graphs and pictographs.
Describe patterns and other relationships from a given data set.
Standard 4: Geometry - November
Solve
problems involving the perimeter and area of triangles and squares.
Determine
the area of a rectangle and create rectangles of a given area.
Find
perimeter and area of squares and rectangles on a grid.
Name
and locate points specified by ordered number pairs on a coordinate
grid.
Standard 5: Measurement - November
Measure
and determine perimeter of polygons to the nearest ½ inch and
centimeter.
Compare
objects according to measurable attributes of length and area in US and
metric units.
Standard 6: Computation - November
Choose
and apply a strategy to solve mathematical and real world problems.
Demonstrate
ability to borrow and carry (trade) in multi-digit addition and
subtraction problems.
Estimate
solutions involving the four basic operations (i.e., estimation by
rounding, front-end estimation, friendly numbers, compatible numbers,
flexible rounding, clustering).
Solve
basic multiplication facts through 12.
Using
paper and pencil, demonstrate basic operations of whole numbers
including addition
Standard 1: Number Sense - December
Compare
large numbers and order 0 – 99,999.
Use estimation strategies to determine reasonable answers in addition.
Recognize
different combinations of currency and coins to $10.00.
Use number properties with any of the four basic operations
(commutative, associative, property of zero and one).
Standard 2: Patterns and Algebra - December
Determine
a missing element in a pattern that uses pictures, geometric shapes or
numbers.
Identify
a rule using addition, subtraction, or multiplication and solve a
problem using the rule (i.e., function boxes, input/.output boxes,
T-charts).
Describe patterns and other relationships using tables and graphs.
Standard 3: Data and Graphs - December
Find
the median, the mode, the smallest and the largest element in a set of
data.
Using statistical data landmarks, draw conclusions and make
interpretations from a given data display.
Standard 4: Geometry - December
Solve
problems involving the perimeter and area of triangles and squares.
Find
perimeter and area of squares and rectangles on a grid.
Name and locate points specified by ordered number pairs on a coordinate
grid.
Make turns, add fractions of turn; relate turns and angles.
Standard 5: Measurement - December
Determine
the area of squares and rectangles on a grid.
Draw and measure line segments to the nearest ½ inch and/or centimeter.
Measure and determine perimeter of polygons to the nearest ½ inch and
centimeter.
Standard 6: Computation - December
Choose
and apply a strategy to solve mathematical and real world problems.
Demonstrate
ability to borrow and carry (trade) in multi-digit addition and
subtraction problems.
Solve basic multiplication facts through 12.
Using paper and pencil, demonstrate basic operations of whole numbers
including addition and subtraction.
Standard 1: Number
Sense - January
Identify
the whole for fractions using hands-on materials and/or visual
representations (base ten blocks, pictures, fraction strips).
Identify
fractional parts of regions (i.e., ½, ¼, 1/10, etc.)
Give
equivalencies between tenths and hundredths in commonly used fractions.
Locate
fractions on a number line.
Standard 2: Patterns
and Algebra - January
Determine
a missing number in a set.
Recognize
and extend a number pattern to solve a problem.
Using
whole numbers show how a change in one number affects a change in another by
addition, subtraction, or multiplication.
Identify
a rule using addition, subtraction, or multiplication and solve a problem
using the rule (i.e., function boxes, input/.output boxes, T-charts).
Standard 3: Data and
Graphs - January
Predict,
determine and support which outcomes are most likely, least likely or
equally likely from flipping a coin, spinning a spinner with 4 congruent
sectors, and rolling a number cube.
Define,
apply and interpret the concepts of probability to determine the outcomes.
Choose
and apply a strategy to solve mathematical and real world problems in
probability and statistics.
Using
statistical data landmarks, organize, construct, read and interpret tables,
line plots, bar graphs and pictographs.
Standard 4: Geometry
- January
Solve
problems involving the perimeter and area of triangles and squares.
Find
perimeter and area of squares and rectangles on a grid.
Name
and locate points specified by ordered number pairs on a coordinate grid.
Make
turns, add fractions of turn; relate turns and angles.
Standard 5:
Measurement - January
Draw
and measure line segments to the nearest ½ inch and/or centimeter.
Measure
and determine perimeter of polygons to the nearest ½ inch and centimeter.
Measure
and determine perimeter of polygons to the nearest ¼ inch and centimeter.
Choose
appropriate units of measure for length, area, volume, capacity, weight,
temperature, and/or time to solve problems.
Standard 6:
Computation - January
Choose
and apply a strategy to solve mathematical and real world problems.
Choose
an operation symbol to make a math sentence true.
Using
pictures, objects and manipulatives, demonstrate addition and subtraction of
commonly used fractions with the same denominators where sums and
differences are equal to or less than a whole (i.e., ½, 1/3, 1/8, 1/10).
Standard 1: Number
Sense - February
Identify
place value of decimals to hundredths.
Identify
and compare fractional parts of a collection of objects.
Identify
the whole for fractions using hands-on materials and/or visual
representations (base ten blocks, pictures, fraction strips).
Identify
fractional parts of regions (i.e., ½, ¼, 1/10, etc.)
Show
division of whole numbers as not commutative (1 digit into 2 digits).
Standard 2: Patterns
and Algebra - February
Determine
a missing element in a pattern that uses pictures, geometric shapes or
numbers.
Identify
a rule using addition, subtraction, or multiplication and solve a problem
using the rule (i.e., function boxes, input/.output boxes, T-charts).
Describe
patterns and other relationships using tables and graphs.
Standard 3: Data and
Graphs - February
Predict,
determine and support which outcomes are most likely, least likely or
equally likely from flipping a coin, spinning a spinner with 4 congruent
sectors, and rolling a number cube.
Define,
apply and interpret the concepts of probability to determine the outcomes.
Choose
and apply a strategy to solve mathematical and real world problems in
probability and statistics.
Given
pictures, describe all possible combinations of matching the elements of two
sets.
Standard 4: Geometry
- February
Name
and locate points specified by ordered number pairs on a coordinate grid.
Make
turns, add fractions of turn; relate turns and angles.
Standard 5:
Measurement - February
Relate
units of measurement of length, area, volume, capacity, weight, and
temperature in US and metric units.
Choose
appropriate units of measure for length, area, volume, capacity, weight,
temperature, and/or time to solve problems.
Standard 6:
Computation - February
Using
money notation, add and subtract decimals in which sums and differences may
exceed $1.00.
Solve
multiplication of 2- or 3-digit numbers by 1-digit numbers.
Using
paper and pencil, demonstrate the four basic operations of whole numbers
including addition, subtraction, multiplication of 2- or 3-digit numbers by
a 1-digit number, and division of a 2-digit number by a 1-digit number.
Standard 1: Number Sense
- March
Identify
place value of decimals to hundredths.
Identify and compare
fractional parts of a collection of objects.
Identify the whole for
fractions using hands-on materials and/or visual representations (base ten
blocks, pictures, fraction strips).
Identify fractional parts
of regions (i.e., ½, ¼, 1/10, etc.)
Standard 2: Patterns and Algebra - March
Determine a missing
element in a pattern that uses pictures, geometric shapes or numbers.
Identify a rule using
addition, subtraction, or multiplication and solve a problem using the rule
(i.e., function boxes, input/.output boxes, T-charts).
Standard 3: Data and Graphs - March
Predict, determine and
support which outcomes are most likely, least likely or equally likely from
flipping a coin, spinning a spinner with 4 congruent sectors, and rolling a
number cube.
Define, apply and
interpret the concepts of probability to determine the outcomes.
Choose and apply a
strategy to solve mathematical and real world problems in probability and
statistics.
Standard 4: Geometry - March
Name and locate points
specified by ordered number pairs on a coordinate grid.
Make turns, add
fractions of turn; relate turns and angles.
Standard 5: Measurement - March
Choose appropriate
units of measure for length, area, volume, capacity, weight, temperature,
and/or time to solve problems.
Relate units of
measurement of length, area, volume, capacity, weight, and temperature in US
and metric units.
Standard 6: Computation - March
Using money notation, add
and subtract decimals in which sums and differences may exceed $1.00.
Solve multiplication of 2-
or 3-digit numbers by 1-digit numbers.
Using paper and pencil,
demonstrate the four basic operations of whole numbers including addition,
subtraction, multiplication of 2- or 3-digit numbers by a 1-digit number,
and division of a 2-digit number by a 1-digit number.
Standard 1: Number Sense
- April
Identify place value in
decimals to hundredths
Identify and compare
fractional parts of a collection of objects.
Identify place value to
millions
Standard 2: Patterns and
Algebra - April
Complete patterns of
shapes and numbers (5th grade CSAP test item).
Recognize and continue a
geometric pattern (5th grade CSAP test item).
Use Function/Rate tables
to observe and explain how a change in one quantity can produce a change in
another (e.g. the relationship between the number of bicycles and the number
of wheels).
Standard 3: Data and
Graphs
- April
Use statistical landmarks,
organize, construct, read and interpret tables, line plots, bar graphs and
pictographs.
Standard 4: Geometry
- April
Recognize geometric
shapes and concepts in other curricula.
Standard 5: Measurement
- April
Use a ruler to measure
distance (5th grade CSAP test item).
Choose appropriate units
of measure for length, area, volume, capacity, weight, temperature, and/or
time to solve problems.
Explain clearly the
strategy used and the solution to mathematical and real-world problems
through written and oral communication.
Standard 6: Computation
- April
Review computation of
whole numbers without context (addition, subtraction, multiplication,
division) (5th grade standard and CSAP test item).
Given a real-world problem solving situation, use an
appropriate method to solve the problem (for example, choose which basic
operation will solve a problem and then calculate the problem using said
operation).
Explain clearly the
strategy used and the solution to mathematical and real-world problems
through written and/or oral communication.
Standard 1: Number Sense
- May
Identify place value in
decimals to hundredths
Identify and compare
fractional parts of a collection of objects.
Identify place value to
millions.
Give equivalent names for
numbers, expanded notation to one million.
Standard 2: Patterns and
Algebra - May
Complete patterns of
shapes and numbers (5th grade CSAP test item).
Recognize and continue a
geometric pattern (5th grade CSAP test item).
Use Function/Rate tables
to observe and explain how a change in one quantity can produce a change in
another (e.g. the relationship between the number of bicycles and the number
of wheels).
Use, explain, and
demonstrate an understanding of the four basic operations in real world,
problem-solving situations.
Standard 3: Data and
Graphs - May
Predict, determine and
support which outcomes are most likely, least likely or equally likely from
flipping a coin, spinning a spinner with 4 congruent sectors, and rolling a
number cube.
Standard 4: Geometry -
May
Identify lines of
symmetry, lines of reflection, reflected figures and figures with line
symmetry.
Recognize geometric shapes
and concepts in other curricula.
Standard 5: Measurement
- May
Use a ruler to measure
distance (5th grade CSAP test item).
Determine the appropriate
unit of measure (metric and US customary) when estimating distance,
capacity, and weight.
Standard 6: Computation
- May
Use, explain, draw a
bi-linguistic representation and demonstrate the understanding of the 4
basic operations.
Determine from a
real-world problem when an estimate or exact sum, difference, product or
quotient is acceptable.
Review computation of
whole numbers without context (addition, subtraction, multiplication,
division) (5th grade standard and CSAP test item).
Resources:
National Virtual Library of
Manipulatives (NVLM) - K-12 math support for Number & Operations,
Algebra, Geometry, Measurement, and Data Analysis & Probability
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